This protocol describes a randomized, double-blind, placebo-controlled, multi-center study of the safety and efficacy of Adefovir Dipivoxil (ADV) versus placebo as intensification therapy in combination with Highly Active Anti-Retroviral Therapy (HAART) in the treatment of HIV infected patients. Patients will be eligible for the study if they have been on a stable regimen of HAART for at least 16 weeks prior to screening. Patients must have a CD4 cell count >50/mm3 and plasma HIV 1 RNA > 50 and < 400 copies per ml within 21 days of enrollment. Patients must also have one additional documented historical viral load below the limit of quantification while on current stable HAART prior to screening.